Why is $x^{-1}$ same as $1/x$?

Question

Can someone explain to me why $x$ to negative $1$, i.e. $x^{-1}$, becomes $1$ over $x$? I asked all my teachers who just said it’s the law. I don’t understand it.

Please explain for a complete mathphobe/math illiterate.

Answer 1

Exponentiation follows the law

$$x^mx^n = x^{m+n}$$

If you use $m=1$ and $n=-1$

you get

$$x^1x^{-1} = x^0$$

So it follows that

$$xx^{-1} = 1$$

and

$$x^{-1} = \frac{1}{x}$$